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surface. To dominate this colossus and not to fear being
crushed by it demands a strain which permits neither rest nor
peace till one stands on top of it and surveys the work in its
entirety. Then only, when one has comprehended its spirit, is
it possible to work justly and in peace at the completion of its
With this declaration of willing servitude Jacobi forthwith
became one of the most terrific workers in the history of mathe-
matics. To a timid friend who complained that scientific
research is exacting and likely to impair bodily health, Jacobi
*Of course! Certainly I have sometimes endangered my health
by overwork, but what of it? Only cabbages have no nerves,
no worries. And what do they get out of their perfect well-
In August 1825 Jacobi received his Ph.D. degree for a disser-
tation on partial fractions and allied topics. There is no need to
explain the nature of this - it is not of any great interest and is
now a detail in the second course of algebra or the integral
calculus. Although Jacobi handled the general case of his
problem and showed considerable ingenuity in manipulating
formulae, it cannot be said that the dissertation exhibited any
marked originality or gave any definite hint of the author's
superb talent. Concurrently with his examination for the Ph.D.
degree, Jacobi rounded off his training for the teaching pro-
After his degree Jacobi lectured at the University of Berlin
on the applications of the calculus to curved surfaces and
twisted curves (roughly, curves determined by the intersections
of surfaces). From the very first lectures it was evident that
Jacobi was a born teacher. Later, when he began developing his
own ideas at an amazing speed, he became the most inspiring
mathematical teacher of his time.
Jacobi seems to have been the first regular mathematical
instructor in a university to train students in research by
lecturing on his own latest discoveries and letting the students
see the creation of a new subject taking place before them. He
believed in pitching young men into the icy water to learn to